Do Gödel's theorems imply that intelligence systems may end up in some undecidable situation (that may make them take a wrong decision)?
Your initial statement on the core of AI is rather limited. In general, AI is concerned with modeling human behaviour either by imitation (soft AI) or by replicating the way human cognition works (hard AI). So far there have been some successes with soft AI, as computers can perform tasks that required some "intelligence", though the degree of this intelligence is questionable. This is partly due to the fact that even we as humans don't really have a clear idea what it means for a computer to "understand" something.

But your conclusion is correct: if we build an AI system with human characteristics, then it will make mistakes, just as humans make mistakes. And any system designed by humans (or machines!) will make mistakes. However, not being able to deal with an imperfect world is not really relevant to AI alone: even systems that do not use AI methods will have to face that, and whether a system is suitable for real-time critical applications has got nothing to do with whether it is based on AI or not.

UPDATE: There seem to be two distinct issues at play here: decidability and real-time processing.


Real-time computing (RTC): This is not really related to AI. Even ordinary programmes written in Java are not really safe for RTC, as they could start a garbage collection cycle at any time which pauses execution of the program. Just imagine a reactor core starts overheating just as your controller runs out of memory and garbage collection kicks in, halting the program for a few minutes. If you implement AI methods in RTC-safe systems, that should not be an issue.
Decidability: Your reasoning is that AI systems attempt to mirror human cognition, thus incorporating the ability to make mistakes. This is a more philosophical issue &mdash; if a human can control a system, then an AI system with the same capabilities should be able to do it too. This assumes that we are able to replicate human behaviour (which we are not). There are AI methods which are deterministic, so would come to the same conclusions given identical environments. So I would say that they would not perform worse than non-AI methods. It partly depends what you want to call AI; the distinction between traditional AI and statistical methods keeps getting blurred at present.


To conclude: No, AI methods should be suitable, as they can also be deterministic. It depends on the actual application and method if they are. And, of course, on what you count as AI.